Why trade needed science
Despite the forest of superstition, the growth of commerce and industry pushed science forward. The elegant, impractical habits of the Renaissance did not fit an expanding economy, and scholars began to want a method that could weigh qualities and quantities, theories and opinions alike. Appeal to experiment, the root of Aristotle's approach, was revived. Italian humanism had prized the literary and artistic glories of Greece and Rome, but now attention turned to practical needs. People had to calculate quickly and accurately, count, measure, draw plans, and observe and record. Out of this need came logarithms, analytic geometry, calculating machines, the microscope, the telescope, statistical methods, navigation instruments and astronomical tools. From then on, across western Europe, a growing number of men spent their lives meeting these needs.
Logarithms and the slide rule
In 1614 John Napier in Scotland, and in 1620 Jost Bürgi in Switzerland, each independently devised a system of logarithms, the logic of numbers, by which products, quotients and roots could be found quickly from tables. Tables are computed to a fixed base. Henry Briggs chose 10 and published tables for the numbers from 1 to 20,000, according to the book. With this method the logarithm of a product becomes the sum of two logarithms, and the logarithm of a quotient becomes their difference. William Oughtred (1622) and Edmund Gunter (1624) built slide rules that gave logarithmic results in moments. These inventions saved mathematicians, astronomers, statisticians, navigators and engineers so much time that, in effect, their working lives were doubled. Kepler, who applied the new method to the motions of the planets, praised Napier without knowing that Napier had died three years before. Napier himself had made one bad calculation: he concluded that the world would end between 1688 and 1700.
Harriot, Dee and the Diggeses
Mathematics and astronomy were still joined, since reckoning the heavens, making calendars and guiding ships all required complex astronomical measurement. Thomas Harriot created modern algebra. He introduced the signs for greater than and less than, used small letters in place of capitals for quantities, and devised the useful habit of putting all terms of an equation on one side with zero on the other. As an astronomer he found sunspots, and his observations of Jupiter's moons were made independently of Galileo. Chapman, himself a learned man, called Harriot's knowledge incomparable and endless.
Astronomy still carried traces of astrology. Horary astrology asked whether the stars favored an undertaking at a given hour. Judicial astrology made general predictions, with deliberate vagueness. Natural astrology read individual fates from the birth chart. All of these survive in our own time, and traces appear in Shakespeare's plays, though they do not show his own belief. By astrological lore the moon governed tides and tears and made some men mad or thieving, and each sign of the zodiac ruled a part of the human body.
John Dee shows the mixture of the age. He gazed into a crystal ball, wrote a treatise on the mysteries of the Rosicrucians, and was accused of sorcery against Queen Mary Tudor. He drew maps and charts for Elizabeth, argued for a northwest passage to China, coined the phrase British Empire, lectured on Euclid in Paris before crowds, defended the Copernican theory, urged adoption of the Gregorian calendar (England accepted the pope's reform 170 years later), and died at eighty-one. His life was truly full. His pupil Thomas Digges worked hard to introduce the Copernican theory to England and, before Bruno, declared that the universe is infinite. Thomas and his father Leonard Digges used sighting instruments that count as ancestors of the telescope. Around 1639 William Gascoigne invented the micrometer, which let astronomers calibrate their instruments with unprecedented accuracy. Jeremiah Horrocks, a poor curate from Lancashire who died at twenty-four, argued that the moon's orbit is an ellipse, and predicted and observed a transit of Venus across the sun (the book dates it 1629). His study of the force behind planetary motion helped Newton formulate universal gravitation.
The study of the magnet
Meanwhile the study of terrestrial magnetism was also paving Newton's road. In 1544 the German priest Georg Hartmann, and in 1576 the English compass maker Robert Norman, each independently discovered the dip of the magnetic needle: a needle balanced at its center of gravity tilts from the horizontal at an angle, the angle of dip. Norman's book, The New Attractive, argued that the point toward which the needle turns lies within the earth.
William Gilbert, physician to Elizabeth, took up the subject. He had inherited a fortune from his father, one the queen herself is said to have coveted, and spent it on seventeen years of research and experiment. He then published England's first scientific book, De Magnete. Gilbert placed a small compass needle at various points on a spherical lodestone, marked the direction it took, and extended each line into a great circle. All the circles met at two opposite points, the magnetic poles, which in the case of the earth Gilbert mistook for the geographic poles. He concluded that the earth is itself a huge magnet, which explains why the needle settles in a fixed direction, and showed that an iron bar left for a time in a north-south position becomes magnetic. The needle stood vertical at the poles of the sphere and horizontal midway between them. From this Gilbert reasoned that the dip is steeper nearer the earth's poles. The idea was not quite right, but Henry Hudson's arctic voyage of 1608 largely confirmed it. Gilbert also drew up rules for finding latitude from the angle of dip.
He also studied electricity, which had been little examined since antiquity. He showed that substances besides amber produce the effect when rubbed, and from the Greek word for amber he coined the term electric for the force that deflects a needle. Gilbert believed all the heavenly bodies have magnetic power, and Kepler used that belief to explain the planets' motions. Much of Gilbert's work is an admirable model of the experimental method, and it influenced both science and industry.
Magnetism and the search for a passage
The advance of science showed itself most strikingly in the efforts of adventurers and the curious to find the great magnet for geographic or commercial ends. In 1576 Sir Humphrey Gilbert (no relation to William) published a discourse on a new passage to China, proposing that it could be reached by the northwest, around Canada. That same year Sir Martin Frobisher set out with three small ships to find such a route. One was lost and another turned back, but he pressed on in the twenty-five-ton Gabriel and reached Baffin Land. Fighting broke out with the Inuit, and he returned to England to gather more supplies and men. (The book's final lines here are partly garbled; this summary follows what can be read.)